Rare means uncommon and does not mean secret. There was very little movie footage taken of Tel Aviv in 1949. Of this, very little was digitally upgraded so that it could be posted to YouTube.The Hope Diamond is rare because very few diamonds match its brilliance, weight and clarity, but anyone can see it for free in the Smithsonian Museum.

In that case, the official broadcast of the superbowl was "rare", since there's only one of it, making it uncommon. The fact that it was made widely available should be irrelevant. I doubt that any newscast showed highlights from the game and reffered to it as "rare" footage. A video of which few copies exist may be considered "rare" (such as the original "Lucy" episode), since it's difficult to obtain. This video may have been "rare" at one point, but I'm not sure that it is anymore. (The original video reel may still be rare.)

The Hope diamond can be more accurately described as "unique", since it possesses many features not found in most other diamonds. "Rare" and "uncommon" are not synonyms in every sense of their respective meaning. When you look up a word in the dictionary (which I assume you did), you have to consider the entire context of the entry, and not just latch onto one word therin.